Additionally, ref. [1]} provides for each UTM its complete set of permutations in all five momenta. In practice this means that we do not need to perform any crossing of momenta in the transcendental functions appearing in the basis \(t_e\) , but simply need to identify the UTMs with the correct crossing that matches the crossing of the scalar integral. The variable \(\varepsilon _5\) , however, needs to be treated separately under permutation of momenta since it is not part of the pre-crossed set of UTMs. In particular, its sign changes under odd permutations.
